checkfile=$checkdir/number.proc
arglist=x
# answer must be 'x=123'
image=0
math=0
questiontype=0
!set n=$counter
!if $level =0
    R=$counter
!else
    R=$level
!endif        
    
keuze=!randitem 1,0
exotitle=!record 3 of lang/remarks.$taal
#@ Vergelijkingen met Exponenten
question$n=!record 62 of lang/remarks.$taal
#@ Los op:<br><small><em>bereken dus de waarden van x</em><br>noteer bij meerdere oplossingen iets als:<br><em>x</em>=1 en <em>x</em>=2/3 of zo...<br>en bij breuken graag het antwoord vereenvoudigen.</small>


!if $R=1
#    a^(x+b)+a^(c-x) = d
#    a^x*a^b + a^c*a^-x = d
#    a^(2x)*a^b + a^c = d*a^x
#    a^b*a^(2x) - d*a^x + a^c = 0
#    p=a^x
#    
#    (a^b)*p^2 - d*p + a^c = 0
#    
#    (mp-q)(rp-s)=0
#    mr*p^2+(-qr-sm)*p+qs=0
#    
#    a^b=mr
#    a^c=qs
#    d=qr+sm
#
#    m=a^(b-f) r=a^f
#    s=a^(c-g) q=a^g
#    d=a^g*a^f+a^(c-g)*a^(b-f)

    a=!randitem 2,3,4
    b=!randitem 1,2,3,4,5
    c=!randitem 1,2,3,4,5
    f=!randitem 1,2,3
    g=!randitem 1,2,3
    h=$[$c+$b-$g-$f]
    !if $h<0
	c=$[$f+$g]
    !endif
    h=$[$c+$b-$g-$f]
    j=$[$b+$c]
    d=$[($a^($g+$f) + $a^($h))]
    dis=(sqrt(($d)^2-4*$a^($j)))
    formula$n= $a^{(x+$b)}+$a^{($c-x)}\,\,=\,\,$d
    x1=$[log((($d) + $dis)/(2*$a^$b))/(log($a))]
    x2=$[log((($d) - $dis)/(2*$a^$b))/(log($a))]
    !ifval $x2=$x1
	answer$n=$x1
	texanswer$n=!texmath x = $x1
    !else
	answer$n=$x1,$x2
	texanswer$n=!texmath x_1 = $x1 \wedge x_2 = $x2
    !endif
 !exit
!endif 

!if $R=2
    a=!randitem 2,3,4
    b=!randitem 1,2,3,4,5
    c=!randitem 1,2,3,4,5
    f=!randitem 1,2,3
    g=!randitem 1,2,3
    h=$[$c+$b-($g+$f)]
    d=$[($a^($g+$f) + $a^($h))]
    !if $h<0
	D=!exec pari printtex($a^($g+$f) + $a^($h))    
    !else
	D=$d
    !endif
    j=$[$b+$c]
    dis=(sqrt(($d)^2-4*$a^($j)))
    formula$n= $a^{(x+$b)}+$a^{($c-x)}\,\,=\,\,$D
    x1=$[log((($d) + $dis)/(2*$a^$b))/(log($a))]
    x2=$[log((($d) - $dis)/(2*$a^$b))/(log($a))]
    !ifval $x2=$x1
	answer$n=$x1
	texanswer$n=!texmath x = $x1
    !else
	answer$n=$x1,$x2
	texanswer$n=!texmath x_1 = $x1 \wedge x_2 = $x2
    !endif
 !exit
!endif
!if $R>2
    a=!randitem 2,3,4
    b=!randitem 1,2,3,4,5
    c=!randitem 1,2,3,4,5
    f=!randitem 2,3,4,5
    g=!randitem 2,3,4,5
    d=$g/$f*$a^$b+$f/$g*$a^$c
    D=!exec pari printtex($g/$f*$a^$b+$f/$g*$a^$c)    
    j=$[$b+$c]
    dis=(sqrt(($d)^2-4*$a^($j)))
    formula$n= $a^{(x+$b)}+$a^{($c-x)}\,\,=\,\,$D
    x1=log((($d) + $dis)/(2*$a^$b))/(log($a))
    x2=log((($d) - $dis)/(2*$a^$b))/(log($a))
    tot=!exec maxima $x1; \
    $x2;
    
    x1=!line 1 of $tot
    x2=!line 2 of $tot
    t1=$[$x1]
    t2=$[$x2]
    !if . notin $t1
	x1=$t1
    !else
	x1=!replace internal log by ln in $x1
    !endif
    !if . notin $t2
	x2=$t2
    !else
	x2=!replace internal log by ln in $x2
    !endif
    
    !ifval $x2=$x1
	answer$n=$x1
	texanswer$n=!texmath x = $x1
    !else
	answer$n=$x1,$x2
	x1=!texmath $x1
	x2=!texmath $x2
	texanswer$n= x_1 = $x1 \wedge x_2 = $x2
    !endif
 !exit
!endif
